The two solenoids are identical. Therefore, the self-inductance of the two solenoids is the same.

The formula used: energy stored in the inductor is given by

Where U is the Magnetic energy

L is the self-Inductance

I is the Current

The current in both solenoids is the same. That implies magnetic field energy is also the same.

The power dissipated as heat is given by

Where P is the power

I is the current

R is the Resistance

The time constant is given by

Where t is the time constant

L is the self-Inductance

R is resistance is given by

Where ρ is the resistivity

l is the length of the wire

A is the Area of cross section

The two solenoids are differed by the Area of the cross section A.

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Thus, the time constant and Joule heat is different for the two solenoids. And self-inductance and magnetic field are the same for the both.